New Game +
Finish the game with any character. When you start a new game, you'll retain all stats, items, and money.
Battle Bosses Again
Beat the Almighty and save your game load it back up and where the bosses were before there will be a black crystal to open and fight the boss again.
Unlock Characters
Beat the game once. DO NOT START A NEW GAME. Just load the old one again and a new map will be open go through it and defeat the Almighty and save at the end. When you turn it back on the character select screen will have arrows at the bottom to switch between the characters.
Ayuta and Mana - Beat the Almighty.
Olgar and Vhati - Beat the Almighty.
New Title Screen
Defeat Piu Piu with all characters to unlock a new title screen.
Fight Piu Piu
Defeat Qualia with all characters.